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Motivic Serre invariants modulo the square of $ \mathbb{L}-1$

Author: Takehiko Yasuda
Journal: Proc. Amer. Math. Soc. 146 (2018), 547-554
MSC (2010): Primary 14D06; Secondary 14E05
Published electronically: September 6, 2017
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Abstract: Motivic Serre invariants defined by Loeser and Sebag are elements of the Grothendieck ring of varieties modulo $ \mathbb{L}-1$. In this paper, we show that we can lift these invariants to modulo the square of $ \mathbb{L}-1$ after tensoring the Grothendieck ring with $ \mathbb{Q}$ under certain assumptions.

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Additional Information

Takehiko Yasuda
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Received by editor(s): January 24, 2017
Received by editor(s) in revised form: April 4, 2017
Published electronically: September 6, 2017
Additional Notes: Most of this work was done during the author’s stay at Institut des Hautes Études Scientifiques. He is grateful for its hospitality and great environment. He also wishes to thank François Loeser for inspiring discussion and helpful comments. This work was partly supported by JSPS KAKENHI grant No. JP15K17510 and JP16H06337.
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 American Mathematical Society

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